A002272 Theta series of 32-dimensional Quebbemann lattice Q_32.

1, 0, 0, 261120, 18947520, 535818240, 8320327680, 83347937280, 622558664640, 3614759362560, 17694184734720, 73337844372480, 272615629589760, 898646461378560, 2752654757806080, 7687895624386560

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.
• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
• G. Nebe and N. J. A. Sloane, Home page for this lattice.
• H.-G. Quebbemann, Lattices with theta-functions for G(sqrt(2)) and linear codes, J. Algebra, 105 (1987), 443-450.
• H.-G. Quebbemann, Modular lattices in Euclidean spaces, J. Number Theory, 54 (1995), 190-202.

Formula

G.f.: b(x)^8 - 192*b(x)^4*d(x) + 576*d(x)^2 where b(x) is the g.f. of A004011 and d(x) is the g.f. of A002288. - Sean A. Irvine, Jul 26 2020